Autistic individuals often have difficulties expressing or controlling emotions and have poor eye contact, among other symptoms. The prevalence of autism is increasing globally, posing a need to address this concern. Current diagnostic systems have particular limitations; hence, some individuals go undiagnosed or the diagnosis is delayed. In this study, an effective autism diagnostic system using electroencephalogram (EEG) signals, which are generated from electrical activity in the brain, was developed and characterized. The pre-processed signals were converted to two-dimensional images using the higher-order spectra (HOS) bispectrum. Nonlinear features were extracted thereafter, and then reduced using locality sensitivity discriminant analysis (LSDA). Significant features were selected from the condensed feature set using Student’s t-test, and were then input to different classifiers. The probabilistic neural network (PNN) classifier achieved the highest accuracy of 98.70% with just five features. Ten-fold cross-validation was employed to evaluate the performance of the classifier. It was shown that the developed system can be useful as a decision support tool to assist healthcare professionals in diagnosing autism.